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Financial stability and economic stability are two different situations, they may cause each other. Some scholars resemble financial stability definition into economic stability, in that case, they are trying to mention the effect of financial instability on macro economy as indicator of financial stability.But this is wrong perception in my opinion, thus, financial stability should be independently defined from its consequence. Thus financial stability is stability of institutions, markets and infrastructure as measured by their respective indicators. If the financial system is stable according to the indicators,it efficiently allocates resources, assesses and manages financial risks, maintains employment levels close to the economy’s natural rate, and eliminates relative price movements of real and financial assets to stabilize monetary and economic levels.

A financial system is stable when it dissipates financial imbalances that arise endogenously or as a result of significant adverse and unforeseeable events. When stable, the system absorbs shocks primarily via self-corrective mechanisms, preventing the adverse events from disrupting the real economy or spread over to other financial systems. Financial stability is paramount for economic growth, as most transactions in the real economy are made through the financial system.

Without financial stability, banks are more reluctant to finance profitable projects, asset prices may deviate significantly from their intrinsic values, and the payment settlement schedule diverges from the norm. Hence, financial stability is essential for maintaining confidence in the economy. Possible consequence of excessive instability includes: bank runs, hyperinflation, or stock market crashes.[2]

The Altman’s z‐score is extensively used in empirical research as a level of firm-level stability for its high correlation with the probability of default. This measure contrasts buffers (capitalization and returns) with risk (volatility of returns), and proven to be accurate at predicting bankruptcies within two years. Despite development of alternative models to predict financial stability Altman’s model remains the most widely used.[3][4]

An alternate model used to measure institution-level stability is the Merton model (also called the asset value model). It evaluates firm’s ability to meet its financial obligations and gauges the overall possibility of default. In this model, an institution’s equity is treated as a call option on its held assets, taking into account the volatility of those assets. Put-call parity is used to price the value of the implied “put” option, which represents the firm's credit risk. Ultimately, the model measures the value of the firm’s assets (weighted for volatility) at the time that the debtholders exercises their “put option” by expecting repayment. Implicitly, the model defines default as when the value of a firm’s liabilities exceeds that of its assets calculate the probability of credit default. In different iterations of the model, the asset/liability level could be set at different threshold levels.

In subsequent researches, the Merton’s model has been modified to capture a wider array of financial activity using credit default swap data. For example, Moody’s uses it in the KMV model to both calculate the probability of credit default and as part of their credit risk management system.(vii) The Distance to Default (DD) is another market-based measure of corporate default risk based on Merton’s model. It measures both solvency risk and liquidity risk at the firm level.

Unfortunately, there is not yet a singular, standardized model for assessing financial system stability and for examining policies.

To measure systemic stability, a number of studies attempt to aggregate firm-level stability measures (z-score and distance to default) into a system-wide evaluation of stability, either by taking a simple average or weighing each measure by the institution’s relative size. However, these aggregate measures fail to account for correlated risks among financial institutions. In other words, the model fails to consider the inter-connectedness between institutions, and that one institution’s failure can lead to a contagion.

The First-to-Default probability, or the probability of observing one default among a number of institutions, has been proposed as a measure of systemic risk for a group of large financial institutions. This measure looks at risk-neutral default probabilities from credit default swap spreads. Unlike distance-to-default measures, the probability recognizes the interconnectedness among defaults of different institutions. However, studies focusing on probabilities of default tend to overlook the ripper effect caused by the failing of a large institution.

Another assessment of financial system stability is Systemic Expected Shortfall (SES), which measures the contribution to systemic risk by individual institutions. SES considers individual leverage level and measures the externalities created from the banking sector when these institutions fail. The model is especially apt at identifying which institutions are systemically relevant and would impact the most on the economy when it fails. One drawback of the SES method is that it is difficult to determine when the systemically-important institutions are likely to fail.[5]

To enhance predictive power, the retrospective SES measure was extended and modified in later research. The enhanced model is called SRISK, which evaluates the expected capital shortfall for a firm in a crisis scenario. To calculate this SRISK, one should first determine the Long-Run Marginal Expected Shortfall (LRMES), which measures the relationship between a firm’s equity returns and the market’s return (estimated using asymmetric volatility, correlation, and copula). Then, the model estimates the drop in the firm’s equity value if the aggregate market experiences a 40% or larger fall in a six-month period to determine how much capital is needed in order to achieve an 8% capital to asset value ratio. In other words, SRISK gives insights into the firm’s percentage of total financial sector capital shortfall. A high SRISK % indicates the biggest losers when a crisis strikes. One implication of the SES indicator is that a firm is considered “systemically risky” if it faces a high probability of capital shortage when the financial sector is weak.[6]

Another gauge of financial stability is the distribution of systemic loss, which attempts to fill some of the gaps of the aforementioned measures. This measure incorporates three key elements: each individual institution’s probability of default, the size of loss given a default, and the contagion resulting from defaults interconnected institutions.[7]